Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N104EB" level="3" n="2" type="chapter" type-free="capitulum">
              <p xml:id="N105D6">
                <s xml:id="N105E3" xml:space="preserve">
                  <pb chead="Prime partis" file="0008" n="8"/>
                quiquarta. ſexquiquinta. / et ſic in infinitum.</s>
              </p>
              <note position="left" xml:id="N105ED" xml:space="preserve">Seqxui-
                <lb/>
              totum.</note>
              <p xml:id="N105F3">
                <s xml:id="N105F4" xml:space="preserve">¶ Unde ſexqui idē eſt quod totū. </s>
                <s xml:id="N105F7" xml:space="preserve">et altera idem eſt
                  <lb/>
                quod medietas. </s>
                <s xml:id="N105FC" xml:space="preserve">et ſic pportio ſexq̇altera: eſt qua
                  <lb/>
                maiꝰ cõtinet minus ſemel tantū: et medietatē eius
                  <lb/>
                </s>
                <s xml:id="N10602" xml:space="preserve">Sexquitertia vero eſt qua maius continet minus
                  <lb/>
                ſemel tantū: et vnã tertiã eiꝰ. </s>
                <s xml:id="N10607" xml:space="preserve">Et ſexquiquarta: qua
                  <lb/>
                maiꝰ cõtinet minꝰ ſemel tantū: et vnã quartã eius /
                  <lb/>
                et ſic in infinitū. </s>
                <s xml:id="N1060E" xml:space="preserve">¶ Generantur autē ſpecies huius
                  <lb/>
                ꝓportionis iſto modo. </s>
                <s xml:id="N10613" xml:space="preserve">Capiatur ordo naturalis
                  <lb/>
                numerorū incipiendo a binario. </s>
                <s xml:id="N10618" xml:space="preserve">et cõparetur ſecū­
                  <lb/>
                dus primo: et tertius ſecundo: et quartus tertio: et
                  <lb/>
                ſic in infinitū. </s>
                <s xml:id="N1061F" xml:space="preserve">et habebūtur oēs ſpecies huiꝰ ꝓpor­
                  <lb/>
                tionis ſereatim. </s>
                <s xml:id="N10624" xml:space="preserve">¶ Si autē libet infinitas ſexquial­
                  <lb/>
                teras ꝓcreare: capientur in vna linea oēs numeri
                  <lb/>
                excedētes ſe binario: et in alia oēs numeri excedē-
                  <lb/>
                tes ſe ternario: et cõparetur primꝰ īferioris primo
                  <lb/>
                ſuꝑioris: et ſecūdus ſcḋo / et ſic in infinitū </s>
                <s xml:id="N1062F" xml:space="preserve">¶ Si vero
                  <lb/>
                in vno ordine ponantur oēs numeri excedentes ſe
                  <lb/>
                ternario. </s>
                <s xml:id="N10636" xml:space="preserve">et in alio excedētes ſe quaternario: ſcḋa
                  <lb/>
                ſpecies ꝓducetur. </s>
                <s xml:id="N1063B" xml:space="preserve">puta ſexquitertia. </s>
                <s xml:id="N1063E" xml:space="preserve">¶ Si autē in
                  <lb/>
                vno ponãtur oēs excedentes ſe quaternario. </s>
                <s xml:id="N10643" xml:space="preserve">et in
                  <lb/>
                alio quinario ꝓducetur tertia ſpecies: puta ſexq̇-
                  <lb/>
                quarta. </s>
                <s xml:id="N1064A" xml:space="preserve">et ſic in infinitū in aliis ſpeciebus. </s>
                <s xml:id="N1064D" xml:space="preserve">vt patꝫ
                  <lb/>
                in figuris ſequentibus.</s>
              </p>
              <note position="left" xml:id="N10652" xml:space="preserve">Genera-
                <lb/>
              tio ſpēi
                <lb/>
              ſuꝑparti-
                <lb/>
              cularis.</note>
              <xhtml:table xml:id="N1065C">
                <xhtml:tr xml:id="N1065D">
                  <xhtml:td xml:id="N1065E" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <note position="left" xml:id="N10660" xml:space="preserve">Gñatio
                <lb/>
              ſexquial­
                <lb/>
              terum.</note>
              <xhtml:table xml:id="N10668">
                <xhtml:tr xml:id="N10669">
                  <xhtml:td xml:id="N1066A" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <note position="left" xml:id="N1066C" xml:space="preserve">Genera-
                <lb/>
              tio ſexq̇-
                <lb/>
              tertiarū.</note>
              <xhtml:table xml:id="N10674">
                <xhtml:tr xml:id="N10675">
                  <xhtml:td xml:id="N10676" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <p xml:id="N10678">
                <s xml:id="N10679" xml:space="preserve">¶ Proportio ſuprapartiens infinitas habet ſpe­
                  <lb/>
                cies: videlicet ſuꝑbipartiēs tertias: ſuꝑbipartiēs
                  <lb/>
                quītas: ſuꝑtripartiens quartas: et ſic in infinitum
                  <lb/>
                </s>
                <s xml:id="N10681" xml:space="preserve">¶ Unde ꝓportio ſuꝑbipartiēs tertias eſt qua ma­
                  <lb/>
                ius continet minus ſemel tantū: et duas tertias mi­
                  <lb/>
                noris. </s>
                <s xml:id="N10688" xml:space="preserve">Unde in quolibet noīe huiꝰ ſpeciei ponūtur
                  <lb/>
                duo numeri. </s>
                <s xml:id="N1068D" xml:space="preserve">Primus numerus denotat numerū
                  <lb/>
                partiū aliquotaꝝ. </s>
                <s xml:id="N10692" xml:space="preserve">Et ſecūdus denotat denoīatio­
                  <lb/>
                nes illaꝝ. </s>
                <s xml:id="N10697" xml:space="preserve">vt cū dicimus ſuꝑbipartiens tertias. ly
                  <lb/>
                bi. dicit numeꝝ partiū aliquotarū. </s>
                <s xml:id="N1069C" xml:space="preserve">quas dicit eſſe
                  <lb/>
                duas. </s>
                <s xml:id="N106A1" xml:space="preserve">et ly tertias dicit / illas eſſe tertias partes nu­
                  <lb/>
                meri mīoris. </s>
                <s xml:id="N106A6" xml:space="preserve">et ſic exēplifica in aliis. </s>
                <s xml:id="N106A9" xml:space="preserve">¶ Generãtur
                  <lb/>
                autē infinite ſpecies huius ꝓportionis iſto modo
                  <lb/>
                </s>
                <s xml:id="N106AF" xml:space="preserve">Capiatur in vna ſerie naturalis ordo numeroruꝫ
                  <lb/>
                incipiēdo a ternario. </s>
                <s xml:id="N106B4" xml:space="preserve">et in alia oēs impares īcipiē­
                  <lb/>
                do a quinario. </s>
                <s xml:id="N106B9" xml:space="preserve">et ↄ̨paret̄̄ primꝰ vniꝰ ordinis ṗmo
                  <lb/>
                alteriꝰ.
                  <note position="left" xlink:href="note-0008-01a" xlink:label="note-0008-01" xml:id="N106CF" xml:space="preserve">Genera-
                    <lb/>
                  tio ſpeci­
                    <lb/>
                  ei ſupra-
                    <lb/>
                  partietꝪ.</note>
                </s>
                <s xml:id="N106C3" xml:space="preserve">et ſecundus ſecūdo et ſic in īfinitū et habebū­
                  <lb/>
                tur īfinite ſpecies huiꝰ ꝓportiõis. </s>
                <s xml:id="N106C8" xml:space="preserve">vt ptꝫ in figura</s>
              </p>
              <xhtml:table xml:id="N106DB">
                <xhtml:tr xml:id="N106DC">
                  <xhtml:td xml:id="N106DD" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <p xml:id="N106DF">
                <s xml:id="N106E0" xml:space="preserve">¶ Proportio auteꝫ multiplex ſuperparticularis
                  <lb/>
                multas habet ſpecies. </s>
                <s xml:id="N106E5" xml:space="preserve">puta duplã ſexquialteram
                  <lb/>
                duplã ſexquitertiã, triplã ſexquialterã, triplã ſex­
                  <lb/>
                quitertiã, et ſic in infinitū: quartū ſpecierū diffini­
                  <lb/>
                tiones patent ex dictis.
                  <note position="left" xlink:href="note-0008-02a" xlink:label="note-0008-02" xml:id="N1071A" xml:space="preserve">Genera-
                    <lb/>
                  tio ſpēi
                    <lb/>
                  multipli­
                    <lb/>
                  cis ſuper­
                    <lb/>
                  particu-
                    <lb/>
                  laris.</note>
                </s>
                <s xml:id="N106F3" xml:space="preserve">¶ Generantur autē īfinite
                  <lb/>
                ſpecies eiꝰ hoc modo. </s>
                <s xml:id="N106F8" xml:space="preserve">Capiatur in vno ordine na­
                  <lb/>
                turalis ſeries numeroꝝ incipiendo a binario. </s>
                <s xml:id="N106FD" xml:space="preserve">et in
                  <lb/>
                alio ordine capiãtur oēs nūeri excedentes ſe q̇na-
                  <lb/>
                rio: a q̇nario exordiendo. </s>
                <s xml:id="N10704" xml:space="preserve">et cõparãdo primū vniꝰ
                  <lb/>
                ordinis. </s>
                <s xml:id="N10709" xml:space="preserve">primo alteriꝰ: cõſtabitur prima ſpecies. </s>
                <s xml:id="N1070C" xml:space="preserve">et
                  <lb/>
                referendo ſecundum ſecundo. / educetur ſecunda. / et
                  <lb/>
                ſic in infinitum. </s>
                <s xml:id="N10713" xml:space="preserve">vt patet in figura.</s>
              </p>
              <xhtml:table xml:id="N1072A">
                <xhtml:tr xml:id="N1072B">
                  <xhtml:td xml:id="N1072C" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <cb chead="Capitulū ſecundū."/>
              <p xml:id="N10730">
                <s xml:id="N10731" xml:space="preserve">¶ Proportio vero multiplex ſuꝑparticularis īfi­
                  <lb/>
                nitas habet ſpecies: quarū q̄libet in infinitas etiã
                  <lb/>
                patit̄̄ ſpecies. </s>
                <s xml:id="N10738" xml:space="preserve">puta duplã ſuꝑparticularē: triplaꝫ
                  <lb/>
                ſuꝑparticularē quadruplã ſuꝑparticularē: et ſic in
                  <lb/>
                infinitū. </s>
                <s xml:id="N1073F" xml:space="preserve">¶ Unde ad ꝓcreandas infinitas duplas
                  <lb/>
                ſuꝑparticularis: capiant̄̄ due ſeries numerorū. </s>
                <s xml:id="N10744" xml:space="preserve">et
                  <lb/>
                in prima ponat̄̄ naturalis ſeries numeroꝝ incipi­
                  <lb/>
                endo a binario. </s>
                <s xml:id="N1074B" xml:space="preserve">in alia vero ponãtur oēs numeri
                  <lb/>
                impares a quīario inchoãdo. </s>
                <s xml:id="N10750" xml:space="preserve">et tūc referēdo primū
                  <lb/>
                inferioris ṗmo ſuperioris: et ſcḋm inferioris: ſcḋo
                  <lb/>
                ſuperioris: et ſic cõſequēter: habebūtur infinite ſpe­
                  <lb/>
                cies huiꝰ duple ſuꝑparticularis. </s>
                <s xml:id="N10759" xml:space="preserve">¶ Sed ad ꝓducē­
                  <lb/>
                das īfinitas triplas ſuꝑparticulares: cõſtituat̄̄ in
                  <lb/>
                ṗma ſerie naturalis ordo nūeroꝝ ſemota vnitate
                  <lb/>
                et in ſcḋa capiant̄̄ oēs nūeri excedētes ſe ternario
                  <lb/>
                incipiēdo a ſeptenario: tūc modo iã ſepiꝰ dicto: re­
                  <lb/>
                ferendo nūeros: infinitas triplas ſuperparticula­
                  <lb/>
                res educes. </s>
                <s xml:id="N10768" xml:space="preserve">¶ A generandas vero īfinitas quadru­
                  <lb/>
                plas ſuperparticulares: ↄ̨ſtituat̄̄ naturalis ſeries
                  <lb/>
                numeroꝝ a ṗmo nūero īchoãdo in linea ſuperiori
                  <lb/>
                in īferiori vero ordinet̄̄ quedã ſeries numeroꝝ: cõ­
                  <lb/>
                tinue excedētiū ſe q̈ternario īchoãdo a nouenario
                  <lb/>
                </s>
                <s xml:id="N10774" xml:space="preserve">¶ Ad generandã autē ſequentē ſpeciē: puta quītu­
                  <lb/>
                plã ſuperparticularē: capias ꝓ primo ordine na-
                  <lb/>
                turale ſeriē numerorū: ꝙ̄ ꝓ qualibet ſpecie debes
                  <lb/>
                capere. </s>
                <s xml:id="N1077D" xml:space="preserve">et ꝓ ſcḋo oēs numeros excedētes ſe q̇nario
                  <lb/>
                incipiēdo ab vndenario. </s>
                <s xml:id="N10782" xml:space="preserve">et pro ſequēti ſpecie puta
                  <lb/>
                ſextupla ſuperparticulari: capiant̄̄ oēs numeri ex­
                  <lb/>
                cedētes ſe ſenario: incipiēdo a tridenario numero
                  <lb/>
                ꝓ alia excedētes ſe ſeptenario: īchoãdo a quīdena­
                  <lb/>
                rio. </s>
                <s xml:id="N1078D" xml:space="preserve">et ſic in īfinitū. </s>
                <s xml:id="N10790" xml:space="preserve">vt ptꝫ in figuris ſequentibus.</s>
              </p>
              <note position="right" xml:id="N10793" xml:space="preserve">Gñatio
                <lb/>
              duplarū
                <lb/>
              ſuꝑparti­
                <lb/>
              culariuꝫ.</note>
              <xhtml:table xml:id="N1079D">
                <xhtml:tr xml:id="N1079E">
                  <xhtml:td xml:id="N1079F" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <note position="right" xml:id="N107A1" xml:space="preserve">Triplaꝝ
                <lb/>
              ſuꝑparti­
                <lb/>
              culariū.</note>
              <xhtml:table xml:id="N107A9">
                <xhtml:tr xml:id="N107AA">
                  <xhtml:td xml:id="N107AB" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <note position="right" xml:id="N107AD" xml:space="preserve">Qua­
                <lb/>
              druplaꝝ
                <lb/>
              ſuꝑparti­
                <lb/>
              culariuꝫ.</note>
              <xhtml:table xml:id="N107B7">
                <xhtml:tr xml:id="N107B8">
                  <xhtml:td xml:id="N107B9" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <p xml:id="N107BB">
                <s xml:id="N107BC" xml:space="preserve">¶ Proportio vero multiplex ſuprapartiēs infini­
                  <lb/>
                tas habet ſpecies: vt dupla ſuprabipartiēs ṫcias
                  <lb/>
                tripla ſuprabipartiēs tertias: et ſic in īfinitū. </s>
                <s xml:id="N107C3" xml:space="preserve">coa-
                  <lb/>
                dunãdo oēs ſpecies ꝓportiõis multiplicis cū q̈li-
                  <lb/>
                bet ſuprapartiēte. </s>
                <s xml:id="N107CA" xml:space="preserve">et ecõuerſo. </s>
                <s xml:id="N107CD" xml:space="preserve">Et īfinitas ſimiliter
                  <lb/>
                habet ſpecies: quaꝝ q̄libet in infinitas etiã partit̄̄
                  <lb/>
                ſpecies: vt puta dupla ſuprapartiēs: in duplã ſu-
                  <lb/>
                prabipartientē tertias: in duplã ſuprabipartiētē
                  <lb/>
                quītas: in duplã ſuprabipartientē quartas. </s>
                <s xml:id="N107D8" xml:space="preserve">et ſic
                  <lb/>
                in īfinitū. </s>
                <s xml:id="N107DD" xml:space="preserve">¶ Generant̄̄ aūt dupla ſuperpartiēs iſto
                  <lb/>
                modo. </s>
                <s xml:id="N107E2" xml:space="preserve">Cõſtituat̄̄ naturalis ſeries nūeroꝝ īcipiēdo
                  <lb/>
                a ternario: q̄ ſemꝑ debet eſſe ṗma in q̈libet ſpecie
                  <lb/>
                tali: et in linea īferiori ponant̄̄ oēs nūeri: excedētes
                  <lb/>
                ſe ternario inchoãdo ab octonario. </s>
                <s xml:id="N107EB" xml:space="preserve">¶ Pro gene-
                  <lb/>
                ratiõe vero triple ſuprapartiētis: in ſcḋa ſerie po­
                  <lb/>
                nant̄̄ oēs nūeri excedētes ſe q̈ternario īcipiēdo ab
                  <lb/>
                vndenario. </s>
                <s xml:id="N107F4" xml:space="preserve">¶ Pro generatiõe aūt q̈druple ſupra­
                  <lb/>
                pariētꝪ: ponãtur in ſcḋa ſerie oēs nūeri. </s>
                <s xml:id="N107F9" xml:space="preserve">excedētes
                  <lb/>
                ſe q̇nario: īcipiēdo a q̈tuordecim. </s>
                <s xml:id="N107FE" xml:space="preserve">Et ꝓ ſequēti ſpe-
                  <lb/>
                cie: capiant̄̄ oēs excedētes ſe ſenario. </s>
                <s xml:id="N10803" xml:space="preserve">et ꝓ alia ſepte­
                  <lb/>
                nario. </s>
                <s xml:id="N10808" xml:space="preserve">et ſic in īfinitū. </s>
                <s xml:id="N1080B" xml:space="preserve">vt ptꝫ in figuris ſequentibus</s>
              </p>
              <note position="right" xml:id="N1080E" xml:space="preserve">Gñatio
                <lb/>
              duplarū
                <lb/>
              ſupraꝑ-
                <lb/>
              tientiū.</note>
              <xhtml:table xml:id="N10818">
                <xhtml:tr xml:id="N10819">
                  <xhtml:td xml:id="N1081A" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <note position="right" xml:id="N1081C" xml:space="preserve">Gñatio
                <lb/>
              triplarū
                <lb/>
              ſupraꝑti-
                <lb/>
              entium.</note>
              <xhtml:table xml:id="N10826">
                <xhtml:tr xml:id="N10827">
                  <xhtml:td xml:id="N10828" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
            </div>
            <div xml:id="N1082A" level="3" n="3" type="chapter" type-free="capitulum"> </div>
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